Performance of Solar
Collectors
The thermal performance of solar collectors can be determined by the detailed
analysis of the optical and thermal characteristics of the collector materials
and collector design, as outlined in Chapter 3, or by experimental performance
testing under control conditions. It should be noted that the accuracy of the
heat transfer analysis depends on uncertainties in the determination of the heat
transfer coefficients, which is difficult to achieve, due to the non-uniform temperature boundary conditions that exist in solar collectors. Such analysis is
usually carried out during the development of prototypes, which are then tested
under defined environmental conditions. In general, experimental verification
of the collector characteristics is necessary and should be done on all collector models manufactured. In some countries, the marketing of solar collectors
is permitted only after test certificates are issued from certified laboratories to
protect the customers.
A number of standards describe the testing procedures for the thermal performance of solar collectors. The most well known are the ISO 9806-1:1994
(ISO, 1994) and the ANSI/ASHRAE Standard 93:2003 (ANSI/ASHRAE, 2003).
These can be used to evaluate the performance of both flat-plate and concentrating solar collectors. The thermal performance of a solar collector is determined partly by obtaining values of instantaneous efficiency for different
combinations of incident radiation, ambient temperature, and inlet fluid temperature. This requires experimental measurement of the rate of incident solar
radiation falling onto the solar collector as well as the rate of energy addition
to the transfer fluid as it passes through the collector, all under steady-state or
quasi-steady-state conditions. In addition, tests must be performed to determine
the transient thermal response characteristics of the collector. The variation of
steady-state thermal efficiency with incident angles between the direct beam
and the normal to collector aperture at various sun and collector positions is
also required.

219

220 Performance of Solar Collectors
ISO 9806-1:1994 and ASHRAE Standard 93:2003 give information on testing solar energy collectors using single-phase fluids and no significant internal
storage. The data can be used to predict the collector performance in any location and under any weather conditions where load, weather, and insolation are
known.
Solar collectors can be tested by two basic methods: under steady-state conditions or using a dynamic test procedure. The former method is widely used
and the test procedures are well documented in the aforementioned standards for
glazed collectors and in ISO 9806-3:1995 (ISO, 1995b) for unglazed collectors.
For steady-state testing, the environmental conditions and collector operation
must be constant during the testing period. For clear, dry locations, the required
steady environmental conditions are easily satisfied and the testing period requires
only a few days. In many locations of the world, however, steady conditions may
be difficult to achieve and testing may be possible only in certain periods of the
year, mainly during summertime, and even then, extended testing periods may
be needed. For this reason, transient or dynamic test methods have been developed. Transient testing involves the monitoring of collector performance for a
range or radiation and incident angle conditions. Subsequently, a time-dependent
mathematical model is used to identify from the transient data the collector performance parameters. An advantage of the transient method is that it can be used
to determine a wider range of collector performance parameters than the steadystate method. The dynamic test method is adopted by EN 12975-1 standard. The
European standards are generally based on the ISO ones but are stricter. These are
briefly introduced in Section 4.8.
To perform the required tests accurately and consistently, a test ring is
required. Two such rings can be used: closed and open loop collector test rings,
as shown in Figures 4.1 and 4.2, respectively. For the tests, the following parameters need to be measured:
1. Global solar irradiance at the collector plane, Gt.
2. Diffuse solar irradiance at the collector aperture.
3. Air speed above the collector aperture.
4. Ambient air temperature, Ta.
5. Fluid temperature at the collector inlet, Ti.
6. Fluid temperature at the collector outlet, To.

7. Fluid flow rate, m.
In addition, the gross collector aperture area, Aa, is required to be measured
with certain accuracy. The collector efficiency, based on the gross collector
aperture area, is given by
η

 p (To  Ti )
mc
Aa Gt

(4.1)

In this chapter, the steady-state test method is thoroughly described. The
dynamic method is presented later in the chapter.

4.1 Collector thermal efficiency
The collector performance test is performed under steady-state conditions, with
steady radiant energy falling on the collector surface, a steady fluid flow rate,
and constant wind speed and ambient temperature. When a constant inlet fluid
temperature is supplied to the collector, it is possible to maintain a constant

222 Performance of Solar Collectors
outlet fluid temperature from the collector. In this case, the useful energy gain
from the collector is calculated from

 p (To  Ti )
Qu  mc

(4.2)

From Chapter 3, we have seen that the useful energy collected from a solar
collector is given by

Qu  Aa FR [Gt (τα )n  U L (Ti  Ta ) ]

(4.3)

Moreover, the thermal efficiency is obtained by dividing Qu by the energy input
(AaGt):

 T  Ta 

η  FR (τα )n  FRU L  i
 Gt 

(4.4)

During testing, the collector is mounted in such a way as to face the sun perpendicularly; as a result, the transmittance-absorptance product for the collector
corresponds to that of beam radiation at normal incidence. Therefore, the term
()n is used in Eqs. (4.3) and (4.4) to denote that the normal transmi­ttanceabsorptance product is used.
Similarly, for concentrating collectors, the following equations from
Chapter 3 can be used for the useful energy collected and collector efficiency:

Qu  FR [GB ηo Aa  Ar U L (Ti  Ta ) ]
η  FR ηo 

FRU L (Ti  Ta )
CGB

(4.5)
(4.6)

Notice that, in this case, Gt is replaced by GB, since concentrating collectors
can utilize only beam radiation (Kalogirou, 2004).
For a collector operating under steady irradiation and fluid flow rate, the
factors FR, ()n, and UL are nearly constant. Therefore, Eqs. (4.4) and (4.6)
plot as a straight line on a graph of efficiency versus the heat loss parameter
(Ti  Ta)/Gt for the case of flat-plate collectors and (Ti  Ta)/GB for the case of
concentrating collectors (see Figure 4.3). The intercept (intersection of the line
with the vertical efficiency axis) equals FR()n for the flat-plate collectors and
FRno for the concentrating ones. The slope of the line, i.e., the efficiency difference divided by the corresponding horizontal scale difference, equals FRUL
and FRUL/C, respectively. If experimental data on collector heat delivery at
various temperatures and solar conditions are plotted with efficiency as the vertical axis and T/G (Gt or GB is used according to the type of collector) as the
horizontal axis, the best straight line through the data points correlates the collector performance with solar and temperature conditions. The intersection of
the line with the vertical axis is where the temperature of the fluid entering the

Collector Thermal Efficiency 223
Flat-plate collector
η

Concentrating collector
η

Intercept � FR (τα)n

Intercept � FR ηo

Slope � �FRUL/C
Slope � �FRUL

∆T/Gt

∆T/GB

Figure 4.3 Typical collector performance curves.

collector equals the ambient temperature and collector efficiency is at its maximum. At the intersection of the line with the horizontal axis, collector efficiency
is zero. This condition corresponds to such a low radiation level, or such a high
temperature of the fluid into the collector, that heat losses equal solar absorption and the collector delivers no useful heat. This condition, normally called
stagnation, usually occurs when no fluid flows in the collector. This maximum
temperature (for a flat-plate collector) is given by
Tmax 

Gt (τα )n
 Ta
UL

(4.7)

As can be seen from Figure 4.3, the slope of the concentrating collectors is
much smaller than the one for the flat-plate. This is because the thermal losses
are inversely proportional to the concentration ratio, C. This is the greatest
advantage of the concentrating collectors, i.e., the efficiency of concentrating
collectors remains high at high inlet temperature; this is why this type of collector is suitable for high-temperature applications.
A comparison of the efficiency of various collectors at irradiance levels of
500 W/m2 and 1000 W/m2 is shown in Figure 4.4 (Kalogirou, 2004). Five representative collector types are considered:
l

As seen in Figure 4.4, the higher the irradiation level, the better is the efficiency, and the higher-performance collectors, such as the CPC, ETC, and

224 Performance of Solar Collectors
0.9
0.8

Efficiency

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

10

20

30

40

50

60

70

80

90

Temperature difference [Ti�Ta] (°C)
FPC-1000

AFP-1000

CPC-1000

ETC-1000

PTC-1000

FPC-500

AFP-500

CPC-500

ETC-500

PTC-500

Figure 4.4 Comparison of the efficiency of various collectors at two irradiation levels:
500 and 1000 W/m2.

PTC, retain high efficiency, even at higher collector inlet temperatures. It
should be noted that the radiation levels examined are considered as global
radiation for all collector types except the PTC, for which the same radiation
values are used but considered as beam radiation.
In reality, the heat loss coefficient, UL, in Eqs. (4.3)–(4.6) is not constant
but is a function of the collector inlet and ambient temperatures. Therefore,

FRU L  c1  c2 (Ti  Ta )

(4.8)

Applying Eq. (4.8) in Eqs. (4.3) and (4.5), we have the following.
For flat-plate collectors.

Qu  Aa FR [(τα )n Gt  c1 (Ti  Ta )  c2 (Ti  Ta )2 ]

(4.9)

and for concentrating collectors.

Qu  FR [GB ηo Aa  Ar c1 (Ti  Ta )  Ar c2 (Ti  Ta )2 ]

(4.10)

Therefore, for flat-plate collectors, the efficiency can be written as

η  FR (τα )  c1

(Ti  Ta )
(T  Ta )2
 c2 i
Gt
Gt

(4.11)

and if we denote co  FR() and x  (Ti  Ta)/Gt, then

η  co  c1 x  c2 Gt x 2

(4.12)

Collector Thermal Efficiency 225
And, for concentrating collectors, the efficiency can be written as

By comparing Eqs. (4.15) and (4.16), we can see that flat-plate collectors
usually have a higher intercept efficiency because their optical characteristics
are better (no reflection losses), whereas the heat loss coefficients of the concentrating collectors are much smaller because these factors are inversely proportional to the concentration ratio.
Equations (4.11) and (4.13) include all important design and operational
factors affecting steady-state performance, except collector flow rate and solar
incidence angle. Flow rate inherently affects performance through the average
absorber temperature. If the heat removal rate is reduced, the average absorber
temperature increases and more heat is lost. If the flow is increased, collector absorber temperature and heat loss decrease. The effect of the solar incidence angle is accounted for by the incidence angle modifier, examined in
Section 4.2.

4.1.1 Effect of Flow Rate
Experimental test data can be correlated to give values of FR()n and FRUL
for a particular flow rate used during the test. If the flow rate of the collector
is changed from the test value during normal use, it is possible to calculate the
new FR for the new flow rate using Eq. (3.58). A correction for the changed
flow rate can be made if it is assumed that F does not change with flow rate,

4.1.2 Collectors in Series
Performance data for a single panel cannot be applied directly to a series of
connected panels if the flow rate through the series is the same as for the single
panel test data. If, however, N panels of the same type are connected in series
and the flow is N times that of the single panel flow used during the testing,
then the single panel performance data can be applied. If two panels are considered connected in series and the flow rate is set to a single panel test flow,
the performance will be less than if the two panels were connected in parallel
with the same flow rate through each collector. The useful energy output from
the two collectors connected in series is then given by (Morrison, 2001):

Qu  Ac FR [(τα )Gt  U L (Ti  Ta )  (τα )Gt  U L (To1  Ta )]

(4.19)

where To1  outlet temperature from first collector given by
To1 

FR [(τα )Gt  U L (Ti  Ta ) ]
 p
mc

 Ti

(4.20)

Eliminating To1 from Eqs. (4.19) and (4.20) gives


K
Qu  FR1 1  [(τα )1Gt  U L1 (Ti  Ta ) ]

2

(4.21)

where FR1, UL1, and ()1 are the factors for the single panel tested, and K is
K

Ac FR1U L1
 p
mc

(4.22)

Collector Thermal Efficiency 227
For N identical collectors connected in series with the flow rate set to the
single panel flow rate,
FR (τα )
FRU L

 1  (1 ��� K ) N 



F
(
τα
)
series
R1
1

NK


series 

(4.23)

 1  (1  K ) N 

FR1U L1 

NK



(4.24)

If the collectors are connected in series and the flow rate per unit aperture
area in each series line of collectors is equal to the test flow rate per unit aperture area, then no penalty is associated with the flow rate other than an increased
pressure drop from the circuit.

Example 4.1
For five collectors in series, each 2 m2 in area and FR1UL1  4 W/m2-°C at a
flow rate of 0.01 kg/s, estimate the correction factor. Water is circulated through
the collectors.
Solution
From Eq. (4.22),
K

Ac FR1U L1
24

 0.19
 p
0.01  4180
mc

The factor

1  (1  K ) N
1  (1  0.19)5

 0.686
5  0.19
NK

This example indicates that connecting collectors in series without increasing the working fluid flow rate in proportion to the number of collectors results
in significant loss of output.

4.1.3 Standard Requirements
Here, the various requirements of the ISO standards for both glazed and unglazed
collectors are presented. For a more comprehensive list of the requirements and
details on the test procedures, the reader is advised to read the actual standard.

Glazed collectors
To perform the steady-state test satisfactorily, according to ISO 9806-1:1994,
certain environmental conditions are required (ISO, 1994):
1. Solar radiation greater than 800 W/m2.
2. Wind speed must be maintained between 2 and 4 m/s. If the natural
wind is less than 2 m/s, an artificial wind generator must be used.

228 Performance of Solar Collectors
3. Angle of incidence of direct radiation is within 2% of the normal incident angle.
4. Fluid flow rate should be set at 0.02 kg/s-m2 and the fluid flow must be stable within 1% during each test but may vary up to 10% between different tests. Other flow rates may be used, if specified by the manufacturer.
5. To minimize measurement errors, a temperature rise of 1.5 K must be
produced so that a point is valid.
Data points that satisfy these requirements must be obtained for a minimum
of four fluid inlet temperatures, which are evenly spaced over the operating
range of the collector. The first must be within 3 K of the ambient temperature to accurately obtain the test intercept, and the last should be at the maximum collector operating temperature specified by the manufacturer. If water is
the heat transfer fluid, 70°C is usually adequate as a maximum temperature. At
least four independent data points should be obtained for each fluid inlet temperature. If no continuous tracking is used, then an equal number of points
should be taken before and after local solar noon for each inlet fluid temperature. Additionally, for each data point, a pre-conditioning period of at least 15
min is required, using the stated inlet fluid temperature. The actual measurement
period should be four times greater than the fluid transit time through the collector with a minimum test period of 15 min.
To establish that steady-state conditions exist, average values of each parameter should be taken over successive periods of 30 s and compared with the
mean value over the test period. A steady-state condition is defined as the period
during which the operating conditions are within the values given in Table 4.1.

Unglazed collectors
Unglazed collectors are more difficult to test, because their operation is influenced by not only the solar radiation and ambient temperature but also the wind
speed. The last factor influences the collector performance to a great extent,
since there is no glazing. Because it is very difficult to find periods of steady
wind conditions (constant wind speed and direction), the ISO 9806-3:1995
for unglazed collector testing recommends that an artificial wind generator is
used to control the wind speed parallel to the collector aperture (ISO, 1995b).
The performance of unglazed collectors is also a function of the module size
Table 4.1 Tolerance of Measured Parameters for Glazed Collectors
Parameter

Deviation from the mean

Total solar irradiance

50 W/m2

Ambient air temperature

1 K

Wind speed

2–4 m/s

Fluid mass flow rate

1%

Collector inlet fluid temperature

0.1 K

Collector Thermal Efficiency 229
and may be influenced by the solar absorption properties of the surrounding
ground (usually roof material), so to reproduce these effects a minimum module size of 5 m2 is recommended and the collector should be tested in a typical
roof section. In addition to the measured parameters listed at the beginning of
this chapter, the longwave thermal irradiance in the collector plane needs to be
measured. Alternatively, the dew point temperature could be measured, from
which the longwave irradiance may be estimated.
Similar requirements for pre-conditioning apply here as in the case of glazed
collectors. However, the length of the steady-state test period in this case should
be more than four times the ratio of the thermal capacity of the collector to the
 p of the fluid flowing through the collector. In this
thermal capacity flow rate mc
case, the collector is considered to operate under steady-state conditions if, over
the testing period, the measured parameters deviate from their mean values by
less than the limits given in Table 4.2.

Using a solar simulator
In countries with unsuitable weather conditions, the indoor testing of solar collectors with the use of a solar simulator is preferred. Solar simulators are generally
of two types: those that use a point source of radiation mounted well away from
the collector and those with large area multiple lamps mounted close to the collector. In both cases, special care should be taken to reproduce the spectral properties of the natural solar radiation. The simulator characteristics required are also
specified in ISO 9806-1:1994 and the main ones are (ISO, 1994):
1. Mean irradiance over the collector aperture should not vary by more
than 50 W/m2 during the test period.
2. Radiation at any point on the collector aperture must not differ by more
than 15% from the mean radiation over the aperture.
3. The spectral distribution between wavelengths of 0.3 and 3 m must be
equivalent to air mass 1.5, as indicated in ISO 9845-1:1992.
4. Thermal irradiance should be less than 50 W/m2.
5. As in multiple lamp simulators, the spectral characteristics of the lamp
array change with time, and as the lamps are replaced, the characteristics of the simulator must be determined on a regular basis.
Table 4.2 Tolerance of Measured Parameters for Unglazed Collectors
Parameter

Deviation from the mean

Total solar irradiance

50 W/m2

Longwave thermal irradiance

20 W/m2

Ambient air temperature

1 K

Wind speed

0.25 m/s

Fluid mass flow rate

1%

Collector inlet fluid temperature

0.1 K

Incidence angle modifier, Kθ

230 Performance of Solar Collectors
1
0.8
0.6
0.4
0.2
0
0

10

20

30
40
50
Angle of incidence (degrees)

60

70

80

Figure 4.5 Incidence angle modified graph.

4.2 Collector incidence angle modifier
4.2.1 Flat-Plate Collectors
The performance Eqs. (4.9) and (4.11) for flat-plate collectors assume that
the sun is perpendicular to the plane of the collector, which rarely occurs. For
the glass cover plates of a flat-plate collector, specular reflection of radiation
occurs, thereby reducing the () product. The incidence angle modifier, K,
is defined as the ratio of () at some incident angle  to () at normal incidence ()n. According to ISO 9806-1:1994, data are collected for angles of
incidence of approximately 0°, 30°, 45°, and 60° (ISO, 1994). A plot of incidence angle modified against incident angle is shown in Figure 4.5.
If we plot the incidence angle modifier against 1/cos()  1, it is observed
that a straight line is obtained, as shown in Figure 4.6, which can be described
by the following expression:

Kθ 

 1

(τα )
 1  b�o 
 1


(τα )n
 cos (θ)

(4.25)

For a single glass cover, the factor b�o in Eq. (4.25), which is the slope of
the line in Figure 4.6, is about 0.1. A more general expression for the incidence
angle modifier is a second-order equation given by

The equation for the useful energy collected, Eq. (4.9), is also modified in a
similar way.

4.2.2 Concentrating Collectors
Similarly, for concentrating collectors, the performance Eqs. (4.10) and (4.13)
described previously are reasonably well defined as long as the direct beam of
solar irradiation is normal to the collector aperture. For off-normal incidence
angles, the optical efficiency term (o) is often difficult to be described analytically, because it depends on the actual concentrator geometry, concentrator
optics, receiver geometry, and receiver optics, which may differ significantly.
As the incident angle of the beam radiation increases, these terms become
more complex. Fortunately, the combined effect of these parameters at different incident angles can be accounted for with the incident angle modifier. This
is simply a correlation factor to be applied to the efficiency curve and is a function of only the incident angle between the direct solar beam and the outward
drawn normal to the aperture plane of the collector. It describes how the optical efficiency of the collector changes as the incident angle changes. With the
incident angle modifier, Eq. (4.13) becomes

η  FR K θ ηo 

c1 (Ti  Ta ) c2 (Ti  Ta )2

CGB
CGB

(4.28)

If the inlet fluid temperature is maintained equal to ambient temperature,
the incident angle modifier can be determined from

where (Ti  Ta) is the measured efficiency at the desired incident angle and,
for an inlet fluid temperature, equal to the ambient temperature. The denominator in Eq. (4.29) is the test intercept taken from the collector efficiency test
with Eq. (4.13), with [o]n being the normal optical efficiency, i.e., at a normal
angle of incidence.
As an example, the results obtained from such a test are denoted by the
small squares in Figure 4.7. By using a curve-fitting method (second-order
polynomial fit), the curve that best fits the points can be obtained (Kalogirou
et al., 1994):

K θ  1  0.00384(θ)  0.000143(θ)2

(4.30)

For the IST collector, the incidence angle modifier K of the collector given
by the manufacturer is

K θ  cos (θ)  0.0003178(θ)  0.00003985(θ)2

(4.31)

4.3 C
oncentrating collector
acceptance angle
Another test required for the concentrating collectors is the determination of
the collector acceptance angle, which characterizes the effect of errors in the
tracking mechanism angular orientation.
This can be found with the tracking mechanism disengaged and by measuring the efficiency at various out-of-focus angles as the sun is traveling over the
collector plane. An example is shown in Figure 4.8, where the angle of incidence measured from the normal to the tracking axis (i.e., out-of-focus angle)
is plotted against the efficiency factor, i.e., the ratio of the maximum efficiency
at normal incidence to the efficiency at a particular out-of-focus angle.

Collector Time Constant 233
1
0.9

Efficiency factor

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
�4

�3

�2

�1

0

1

2

3

4

Angle of incidence (degrees)

Figure 4.8 Parabolic trough collector acceptance angle test results.

A definition of the collector acceptance angle is the range of incidence angles
(as measured from the normal to the tracking axis) in which the efficiency factor varies by no more than 2% from the value of normal incidence (ASHRAE,
2003). Therefore, from Figure 4.8, the collector half acceptance angle, m, is
0.5°. This angle determines the maximum error of the tracking mechanism.

4.4 Collector time constant
A last aspect of collector testing is the determination of the heat capacity of a
collector in terms of a time constant. It is also necessary to determine the time
response of the solar collector in order to be able to evaluate the transient behavior of the collector and select the correct time intervals for the quasi-steady-state
or steady-state efficiency tests. Whenever transient conditions exist, Eqs. (4.9) to
(4.14) do not govern the thermal performance of the collector, since part of the
absorbed solar energy is used for heating up the collector and its components.
The time constant of a collector is the time required for the fluid leaving
the collector to reach 63.2% of its ultimate steady value after a step change in
incident radiation. The collector time constant is a measure of the time required
for the following relationship to apply (ASHRAE, 2003):
Tof  Tot
1
  0.368
Tof  Ti
e

(4.32)

where
Tot  collector outlet water temperature after time t (°C).
Tof  collector outlet final water temperature (°C).
Ti  collector inlet water temperature (°C).
The procedure for performing this test is as follows. The heat transfer fluid is
circulated through the collector at the same flow rate as that used during collector
thermal efficiency tests. The aperture of the collector is shielded from the solar

234 Performance of Solar Collectors
Tot�Ta

Time when shading is
removed (time zero)

Time when steady
state is re-established

Tof�Ta

0.632[(Tof �Ta)–(Toi�Ta)]
Toi�Ta
Time constant
Time

Figure 4.9 Time constant as specified in ISO 9806-1:1994.

radiation by means of a solar reflecting cover, or in the case of a concentrating
collector, the collector is defocused and the temperature of the heat transfer fluid
at the collector inlet is set approximately equal to the ambient air temperature.
When a steady state has been reached, the cover is removed and measurements
continue until steady-state conditions are achieved again. For the purpose of this
test, a steady-state condition is assumed to exist when the outlet temperature of
the fluid varies by less than 0.05°C per minute (ISO, 1994).
The difference between the temperature of the fluid at the collector outlet at time t and that of the surrounding air (Tot  Ta), (note that, for this test,
Ti  Ta)������������������������������������������������������������������������
is plotted against time, beginning with the initial steady-state condition (Toi  Ta) and continuing until the second steady state has been achieved
at a higher temperature (Tof  Ta), as shown in Figure 4.9.
The time constant of the collector is defined as the time taken for the collector outlet temperature to rise by 63.2% of the total increase from (Toi  Ta)
to (Tof  Ta) following the step increase in solar irradiance at time 0.
The time constant specified in the standard ISO 9806-1:1994, as described
previously, occurs when the collector warms up. Another way to perform this
test, specified in ASHRAE standard 93:2003 and carried out in addition to the
preceding procedure by some researchers, is to measure the time constant during cool-down. In this case, again, the collector is operated with the fluid inlet
temperature maintained at the ambient temperature. The incident solar energy
is then abruptly reduced to 0 by either shielding a flat-plate collector or defocusing a concentrating one. The temperatures of the transfer fluid are continuously monitored as a function of time until Eq. (4.33) is satisfied:

Tot  Ti
1
  0.368
Toi  Ti
e

(4.33)

where Toi  collector outlet initial water temperature (°C).
The graph of the difference between the various temperatures of the fluid in
this case is as shown in Figure 4.10.

Dynamic System Test Method 235
Tot�Ta

Time when shading is Time when steady
employed (time zero) state is re-established

Toi�Ta

0.632[(Toi�Ta)�(Tof�Ta)]

Tof�Ta
Time constant
Time

Figure 4.10 Time constant as specified in ASHRAE 93:2003.

The time constant of the collector, in this case, is the time taken for the
collector outlet temperature to drop by 63.2% of the total increase from
(Toi  Ta) to (Tof  Ta) following the step decrease in solar irradiance at time 0
(ASHRAE, 2003).

4.5 Dynamic system test method
For locations that do not have steady environmental conditions for long periods
of time, the transient or dynamic system test method can be used. This method
involves monitoring the transient response of a collector over a number of days,
which include both clear and cloudy conditions. The performance data obtained
from the dynamic method allow a more detailed characterization of the collector performance in comparison with the steady-state method. The advantages
of the dynamic test method are that the test period is much shorter and can be
conducted at any time of the year under variable weather conditions. After testing, the data collected over the wide range of operating conditions are fitted to
a transient mathematical model of the collector performance. The test data are
measured every 5–10 min. For a glazed collector, the following model for the
transient useful energy collection could be used (Morrison, 2001):

where o, a0, a1, c, and the coefficients K,B and K,D are determined by the correlation of the test measured data.
Equation (4.34) is similar to the second-order equations used for steady-state
testing, presented earlier in this chapter, with the addition of a transient term and
incident angle modifiers for both beam, K,B, and diffuse, K,D, radiation.
Models that are more complex can be used if the testing program can cover
an extended range of operating conditions. In any case, the measured transient
data are analyzed using a procedure that compares a set of model coefficients that

236 Performance of Solar Collectors
minimize the deviation between the measured and predicted output. The method
should be such that the various parameters should be determined as independently as possible. To be able to satisfy this requirement, sufficient data are
needed; therefore, it is required to control the experimental conditions so that
all variables independently influence the operation of the collector at various
periods during testing. Additionally, a wide range of test conditions is required
to determine the incident angle modifiers accurately. An added advantage of
the method is that the equipment required is the same as the steady-state testing shown in Figures 4.1 and 4.2, which means that a test center can have the
same equipment and perform both steady-state and dynamic testing at different
periods of the year, according to the prevailing weather conditions. The primary
difference between the two methods is that, in the dynamic method, the data are
recorded on a continuous basis over a day and averaged over 5–10 min.
Due to the wider range of collector parameters that can be determined with
the dynamic method, it is likely that it may displace the steady-state testing
method, even for locations that have clear and stable climatic conditions.

4.6 C
ollector test results and preliminary
collector selection
Collector testing is required to evaluate the performance of solar collectors and
compare different collectors to select the most appropriate one for a specific
application. As can be seen from Sections 4.1–4.5, the tests show how a collector absorbs solar energy and how it loses heat. They also show the effects of
angle of incidence of solar radiation and the significant heat capacity effects,
which are determined from the collector time constant.
Final selection of a collector should be made only after energy analyses
of the complete system, including realistic weather conditions and loads, have
been conducted for one year. In addition, a preliminary screening of collectors
with various performance parameters should be conducted in order to identify
those that best match the load. The best way to accomplish this is to identify
the expected range of the parameter T/G for the load and climate on a plot of
efficiency  as a function of the heat loss parameter, as indicated in Figure 4.11
(Kalogirou, 2004).
Collector efficiency curves may be used for preliminary collector selection.
However, efficiency curves illustrate only the instantaneous performance of a
collector. They do not include incidence angle effects, which vary throughout the
year; heat exchanger effects; and probabilities of occurrence of Ti, Ta, solar irradiation, system heat loss, or control strategies. Final selection requires the determination of the long-term energy output of a collector as well as performance
cost-effectiveness studies. Estimating the annual performance of a particular collector and system requires the aid of appropriate analysis tools such as f-chart,
Watsun, or TRNSYS. These are presented in Chapter 11, Section 11.5.
The collector performance equations can also be used to estimate the daily
energy output from the collector. This is illustrated by means of Example 4.2.

Example 4.2
Consider a flat-plate collector with the following characteristics:

η  0.76  5.6 [(Ti  Ta )/Gt ]

K θ  1  0.12 [1/ cos (θ)  1]

Find the energy collected during a day with the characteristics shown in
Table 4.3.
Table 4.3 Data Collected for Example 4.2
Time

Ambient temperature, Ta (°C)

Solar radiation, Gt (W/m2)

6

25

100

7

26

150

8

28

250

9

30

400

10

32

600

11

34

800

12

35

950

13

34

800

14

32

600

15

30

400

16

28

250

17

26

150

18

25

100

238 Performance of Solar Collectors
The collector area is 2 m2, located at 35°N latitude, and tilted at 45° from
horizontal. The estimation is done on June 15 and collector inlet temperature is
constant equal to 50°C.
Solution
As the weather conditions are given for every hour, the estimation is performed
on an hourly basis, during which it is considered that the weather conditions
remain constant. The most difficult parameter to consider is Ti, the inlet temperature to the collector, which is dependent on the system and its location. In this
example, this is considered as constant throughout the day and equal to 50°C.
The efficiency  is equal to Qu/AaGt. Therefore,
Qu  Aa Gt [0.76 K θ  5.6(Ti  Ta )/Gt ]

The angle of incidence required for the estimation of the incidence angle
modifier, K, is obtained from Eq. (2.20). The declination on June 15 is 23.35°.
It should be noted that, for the estimation of T/Gt, the radiation used is in
W/m2, whereas for the estimation of Qu irradiation in kJ/m2 is used, obtained
by multiplying W/m2 by 3.6. The results are shown in Table 4.4.
Table 4.4 Results of Example 4.2
Time

Ta (°C)

It (kJ/m2)

T/Gt
(°C-m2/kJ)

 (degrees)

K

Qu (kJ)

6

25

360

0.250

93.9

0

0

7

26

540

0.160

80.5

0.394

0

8

28

900

0.088

67.5

0.807

216.8

9

30

1440

0.050

55.2

0.910

1184.7

10

32

2160

0.030

44.4

0.952

2399.8

11

34

2880

0.020

36.4

0.971

3604.8

12

35

3420

0.016

33.4

0.976

4470.6

13

34

2880

0.020

36.4

0.971

3604.8

14

32

2160

0.030

44.4

0.952

2399.8

15

30

1440

0.050

55.2

0.910

1184.7

16

28

900

0.088

67.5

0.807

216.8

17

26

540

0.160

80.5

0.394

0

18

25

360

0.250

93.9

0

0

Therefore, the total energy collected over the day  19282.8 kJ.
In this example, the use of a spreadsheet program greatly facilitates
estimations.

Quality Test Methods 239

4.7 Quality test methods
As we have seen in Chapter 3, the materials used for the construction of the
collector should be able to withstand, in addition to the effects created because
of the circulating fluid (corrosion, scale deposits, etc.), the adverse effects of
the sun’s ultraviolet radiation, and the collector should have an operation life
of more than 20 years. Solar collectors are also required to withstand cyclic
thermal operation many times a day and extreme operating conditions, such as
freezing, overheating, thermal shocks, external impact due to hail or vandalism, and pressure fluctuations. Most of these factors occur simultaneously.
It is therefore required to perform tests on solar collectors to determine
their quality. In particular, the ability of a collector to resist extreme operating
conditions is examined as specified in International Standard ISO 9806-2:1995
(1995a). This standard applies to all types of solar collectors, including integral
collector storage systems, except tracking concentrating collectors. Collectors
are required to resist a number of influences, which can be clearly identified
and quantified, such as high internal fluid pressures, high temperatures, and
rain penetration, as shown in Table 4.5. The tests are required to be applied in
the sequence specified in Table 4.5 so that possible degradation in one test will
be exposed in a later test.
For many quality tests, the collector is required to operate at the stagnation
temperature. Provided that the collector was tested at a sufficiently high inlet
Table 4.5 Sequence of Quality Tests for Solar Collectors
Sequence

Test

Collector

1

Internal pressure

A

2

High-temperature resistance1

A

3

Exposure

A, B, and C
2

4

External thermal shock

5

Internal thermal shock

A

6

Rain penetration

A

7

Freeze resistance

A

8

Internal pressure (re-test)

A

9

Thermal performance

A

10

Impact resistance

A or B

11

Final inspection

A, B, and C

A

Notes:
1
For organic absorbers, the high-temperature resistance test should be performed first, to determine
the collector stagnation temperature needed for the internal pressure test.
2
The external thermal shock test may be combined with the exposure test.

240 Performance of Solar Collectors
water temperature, the performance equation can be used to determine stagnation temperature. By using Eq. (4.11) and denoting FR() as o,
Tstag  Ta 

c1  c12  4ηo c2 Gt
2c2

(4.35)

4.7.1 Internal Pressure Test
The absorber is pressure tested to assess the extent to which it can withstand
the pressures it might meet in service. For the metallic absorbers, the test pressure, maintained for 10 min, is either the maximum test pressure specified by
the manufacturer or 1.5 times the maximum collector operating pressure stated
by the manufacturer, whichever is lower.
For absorbers made of organic materials (plastics or elastomers), the test
temperature is the maximum temperature the absorber will reach under stagnation conditions. This is because the properties of organic materials are temperature dependent. One of the alternative sets of reference conditions given in
Table 4.6 must be used to determine the test temperature, depending on the climate in which the collector will be used. The test pressure should be 1.5 times
the maximum collector operating pressure specified by the manufacturer and
should be maintained for at least one hour.
For air-heating collectors, the test pressure is 1.2 times the maximum collector operating pressure difference above or below atmospheric pressure, as
specified by the manufacturer, maintained for 10 min.

4.7.2 High-Temperature Resistance Test
This test is intended to assess rapidly whether a collector can withstand high
irradiance levels without failures such as glass breakage, collapse of plastic
cover, melting of plastic absorber, or significant deposits on the collector cover
from out-gassing of the collector material. The test is performed at a temperature equal to the collector stagnation temperature. The test is performed for a
minimum of one hour after a steady state is reached. The conditions required
in this test are as shown in Table 4.6 with the addition of surrounding air speed,
which must be less than 1 m/s.

4.7.3 Exposure Test
The exposure test provides a low-cost indication of the aging effects that are
likely to occur during a longer period of natural aging. In addition, it allows the
collector to “settle,” such that subsequent qualification tests are more likely to
give repeatable results. An empty collector is mounted outdoors and all of its
fluid pipes are sealed to prevent cooling by natural circulation of air except one
pipe, which is left open to permit free expansion of air in the absorber. One of
the alternative sets of reference conditions given in Table 4.7 must be used,
depending on the climate in which the collector will operate. For each class of
reference conditions, the collector is exposed until at least 30 d (which need not
be consecutive) have passed with the minimum irradiation shown in Table 4.7.

4.7.4 External Thermal Shock Test
Collectors from time to time may be exposed to sudden rainstorms on hot, sunny
days, causing a severe external thermal shock. This test is intended to assess the
capability of a collector to withstand such thermal shocks without a failure. An
empty collector is used here, as in previous tests prepared in the same way. An
array of water jets is arranged to provide a uniform spray of water over the collector. The collector is maintained in steady-state operating conditions under a
high level of solar irradiance for a period of 1 h before the water spray is turned
on. It is then cooled by the water spray for 15 min before being inspected. Here
again, one of the alternative sets of reference conditions given in Table 4.7 can
be used, depending on the climate in which the collector will operate, and the
heat transfer fluid must have a temperature of less than 25°C.

4.7.5 Internal Thermal Shock Test
Collectors from time to time may be exposed to a sudden intake of cold heat
transfer fluid on hot, sunny days, causing a severe internal thermal shock. This
could happen, for example, after a period of shutdown, when the installation is
brought back into operation while the collector is at its stagnation temperature.
Table 4.7 Climate Reference Conditions for Exposure Test as Well as for External
and Internal Thermal Shock Tests
Climate parameter

Class A:
Temperate

Class B:
Sunny

Class C:
Very sunny

Global solar irradiance on the collector
plane (W/m2)

850

950

1050

Global daily irradiation on the collector
plane (MJ/m2)

14

18

20

Ambient air temperature (°C)

10

15

20

Note: Values given are minimums for testing.

242 Performance of Solar Collectors
This test is intended to assess the capability of a collector to withstand such thermal shocks without failure. Here again, an empty collector is used, as in previous
tests prepared in the same way; the same reference conditions given in Table 4.7
can be used, depending on the climate in which the collector will operate, and the
heat transfer fluid must have a temperature of less than 25°C.

4.7.6 Rain Penetration
This test is intended to assess the extent to which collectors are substantially
resistant to rain penetration. The collectors must not normally permit the entry
of either free-falling rain or driving rain, either through the glazing seals or from
ventilation holes or drain holes. For this test, the inlet and outlet fluid pipes of
the collector must be sealed, and they must be placed in a test rig at the shallowest angle to the horizontal recommended by the manufacturer. If this angle is
not specified, then the collector can be placed at a tilt of 45° to the horizontal or
less. Collectors designed to be integrated into a roof structure must be mounted
on a simulated roof and have their underside protected. Other collectors must
be mounted in a conventional manner on an open frame. The collector must be
sprayed on all sides using spray nozzles or showers for a test period of 4 h.
For collectors that can be weighed, weighing must be done before and after
the test. After the test, external surfaces of the collector must be wiped dry
before the weighing. During the wiping, transport, and placement on the weighing machine, the angle of inclination of the collector must not be changed appreciably. For collectors that cannot be weighed, the penetration of water into the
collector can be determined only by visual inspection.

4.7.7 Freezing Test
This test is intended to assess the extent to which water-heating collectors that
are claimed to be freeze resistant can withstand freezing and freeze-thaw cycles.
This test is not intended for use with collectors that are filled with antifreeze
fluids. Two test procedures are specified: one for collectors claimed to be freeze
resistant when filled with water and one for collectors claimed to resist freezing
after being drained.
For collectors claimed to be able to withstand freezing, the collector is
mounted in a cold chamber. The collector must be inclined at the shallowest angle
to the horizontal recommended by the manufacturer. If no angle is specified by
the manufacturer, then the collector must be inclined at an angle of 30° to the horizontal. Unglazed collectors must be tested in a horizontal position, unless this is
excluded by the manufacturer. Next, the collector is filled with water at the operating pressure. The cold-chamber temperature is cycled, and at the end of each
cycle, the collector is refilled with water at operating pressure.
For collectors claimed to resist freezing after being drained (i.e., they
employ a drain-down system to protect them from freezing), the collector is
mounted in a cold chamber as before with the same provisions for the collector
inclination. The collector is next filled with water, kept at operating pressure

European Standards 243
for 10 min, then drained using the device installed by the manufacturer. The
contents of the absorber are maintained at 20 2°C for at least 30 min during the freezing part of the cycle and raised to above 10°C during the thawing
part of the cycle, which is again at least of 30 min duration. The collector must
be subjected to three freeze-thaw cycles.

4.7.8 Impact Resistance Test
This is an optional test intended to assess the extent to which a collector can
withstand the effects of heavy impacts, such as those caused by minor vandalism or likely to occur during installation. Heavy impacts may also be caused
by hailstones.
The collector is mounted either vertically or horizontally on a stiff support
that must have a negligible distortion or deflection at the time of impact. Steel
balls with a mass of 150 g are used to simulate the heavy impact. If the collector is
mounted horizontally, then the steel balls are dropped vertically; if it is mounted
vertically, then the impacts are directed horizontally by means of a pendulum.
The point of impact must be no more than 5 cm from the edge of the collector cover and no more than 10 cm from the corner of the collector cover
and must be moved by several millimeters each time the steel ball is dropped.
A steel ball must be dropped onto the collector 10 times from the first test
height, then 10 times from the second test height, and so forth until the maximum test height is reached. The test is stopped when the collector exhibits
some damage or has survived the impact of 10 steel balls at the maximum test
height. The test heights start from 0.4 m up to 2.0 m in steps of 20 cm.
In addition to the preceding quality tests, the ISO developed a range of
material and product quality test standards for solar collectors. The following
specific material test methods standards have been developed:
l

4.8 European standards
In the framework of the European Committee for Standardization, CEN
(Comité Européenne de Normalisation), the operation of a new technical committee dealing with solar thermal collectors and systems has been initiated.
Specifically, CEN/TC 312, “Thermal solar systems and components,” was
created in 1994, following a request of the European Solar Thermal Industry
Federation (ESTIF) to the CEN Central Secretariat. The scope of CEN/TC

244â&#x20AC;&#x192; Performance of Solar Collectors
312 is the preparation of European standards to cover terminology, general
requirements, characteristics, and test methods of thermal solar systems and
components.
The primary aim of the European standards is to facilitate the exchange of
goods and services through the elimination of technical barriers to trade. The use
of standards by industry and social and economic partners is always voluntary.
However, European standards are sometimes related to European legislation
(directives). Furthermore, conformity to such standards may be a presumption
for solar projects to get a subsidy from national renewable energy systems supporting programs (Kotsaki, 2001).
For the elaboration of European technical standards, corresponding national
documents as well as international standards (ISO) have been taken into consideration. It should be noted that, compared to the existing standards, the European
norms under consideration are performing a step forward, since they incorporate
new features, such as quality and reliability requirements.
In April 2001, CEN published eight standards related to solar collectors and
systems testing. With the publication of these European standards, all national
standards related to the same topic were (or have to be) withdrawn by the nations
of the European Community. Most of these standards were revised in 2006.
A complete list of these standards is as follows:
EN 12975-1:2006. Thermal solar systems and components, Solar collectors, Part 1: General requirements. This European standard specifies
requirements on durability (including mechanical strength), reliability,
and safety for liquid-heating solar collectors. It also includes provisions
for evaluation of conformity to these requirements. CEN publication
date: March 29, 2006.
l EN 12975-2:2006. Thermal solar systems and components, Solar collectors, Part 2: Test methods. This European standard establishes test
methods for validating the durability and reliability requirements for
liquid-heating collectors as specified in EN 12975-1. This standard also
includes three test methods for the thermal performance characterization
for liquid-heating collectors. CEN publication date: March 29, 2006.
l EN 12976-1:2006. Thermal solar systems and components, Factory-made
systems, Part 1: General requirements. This European standard specifies
requirements on durability, reliability, and safety for factory-made solar
systems. This standard also includes provisions for evaluation of conformity to these requirements. CEN publication date: January 25, 2006.
l EN 12976-2:2006. Thermal solar systems and components, Factorymade systems, Part 2: Test methods. This European standard specifies
test methods for validating the requirements for factory-made solar systems as specified in EN 12976-1. The standard also includes two test
methods for the thermal performance characterization by means of
whole-system testing. CEN publication date: January 25, 2006.
l ENV 12977-1:2001. Thermal solar systems and components, Custombuilt systems, Part 1: General requirements. This European pre-standard
l

European Standardsâ&#x20AC;&#x192; 245
specifies requirements on durability, reliability, and safety of small and
large custom-built solar heating systems with liquid heat transfer medium
for residential buildings and similar applications. The standard also contains requirements on the design process of large custom-built systems.
CEN publication date: April 25, 2001.
l ENV 12977-2:2001. Thermal solar systems and components, Custombuilt systems, Part 2: Test methods. This European prestandard applies to
small and large custom-built solar heating systems with liquid heat transfer medium for residential buildings and similar applications and specifies test methods for verification of the requirements specified in ENV
12977-1. The standard also includes a method for thermal performance
characterization and system performance prediction of small custom-built
systems by means of component testing and system simulation. CEN
publication date: April 25, 2001.
l ENV 12977-3:2001. Thermal solar systems and components, Custombuilt systems, Part 3: Performance characterization of stores for solar
heating systems. This European pre-standard specifies test methods
for the performance characterization of stores intended for use in small
custom-built systems as specified in ENV 12977-1. CEN publication
date: April 25, 2001.
l EN ISO 9488:1999. Solar energy, Vocabulary (ISO 9488:1999). This
European-International standard defines basic terms relating to solar
energy and has been elaborated in common with ISO. CEN publication
date: October 1, 1999.
The elaboration of these standards has been achieved through a wide
European collaboration of all interested parties, such as manufacturers, researchers, testing institutes, and standardization bodies. Furthermore, these standards
will promote a fair competition among producers of solar energy equipment on
the market, since low-quality/low-price products will be easier to be identified
by customers, based on uniform test reports comparable throughout Europe.
The increased public awareness of the environmental aspects is reinforced by
these standards, which help ensure the quality level for the consumer and provide
more confidence in the new solar heating technology and products available.

4.8.1â&#x20AC;&#x201A; Solar Keymark
The Solar Keymark certification scheme was initiated by the European Solar
Thermal Industry Federation (ESTIF) to avoid internal European trade barriers
due to different requirements in national subsidy schemes and regulations.
Before the European standards and the Solar Keymark were established, solar
thermal products had to be tested and certified according to different national
standards and requirements. The Solar Keymark idea is that only one test and
one certificate are necessary to fulfill all requirements in all EU member states.
The Solar Keymark certification scheme was introduced to harmonize
national requirements for solar thermal products in Europe. The objective is that,
once tested and certified, the product should have access to all national markets.

246 Performance of Solar Collectors
This goal has now been achieved, except for some minor supplementary requirements in a few member states.
The CEN Solar Keymark certification scheme has been available for solar
thermal products in Europe since 2003. The Solar Keymark states conformity
with the European standards for solar thermal products. The CEN keymark is
the pan-European voluntary third-party certification mark, demonstrating to
users and consumers that a product conforms to the relevant European standard
(Nielsen, 2007).
The Solar Keymark is the keymark certification scheme applied specifically
for solar thermal collectors and systems, stating conformity with the following
European standards:
l
l

Products with the Solar Keymark have access to all national subsidy
schemes in EU member states.
l In some member states (e.g., Germany), it is now obligatory that solar
collectors show the Keymark label.
l People expect the Solar Keymark; most collectors sold now are Keymark
certified.
The main elements of the party Keymark certification are:
l

Type testing according to European standards (test samples to be sampled by an independent inspector).
l Initial inspection of factory production control (quality management system at ISO 9001 level).
l Surveillance: annual inspection of factory production control.
l Biannual “surveillance test”: detailed inspection of products.

4.9 Data acquisition systems
Today, most scientists and engineers use personal computers for data acquisition in laboratory research, test and measurement, and industrial automation.
To perform the tests outlined in this chapter as well as whole-system tests, a
computer data acquisition system (DAS) is required.
Many applications use plug-in boards to acquire data and transfer them
directly to computer memory. Others use DAS hardware remote from the PC
that is coupled via a parallel, serial, or USB port. Obtaining proper results from
a PC-based DAS depends on each of the following system elements:
l

Data Acquisition Systems 247
The personal computer is integrated into every aspect of data recording,
including sophisticated graphics, acquisition, control, and analysis. Modems
connected to the Internet or an internal network allow easy access to remote
personal computer-based data recording systems from virtually any place. This
is very suitable when performing an actual solar system monitoring.
Almost every type of transducer and sensor is available with the necessary interface to make it computer compatible. The transducer itself begins to
lose its identity when integrated into a system that incorporates such features
as linearization, offset correction, and self-calibration. This has eliminated the
concern regarding the details of signal conditioning and amplification of basic
transducer outputs.
Many industrial areas commonly employ signal transmitters for control or
computer data handling systems to convert the signal output of the primary sensor into a compatible common signal span. The system required for performing
the various tests described in this chapter, however, needs to be set up by taking
the standard requirements about accuracy of the instruments employed.
The vast selection of available DAS hardware make the task of configuring a data acquisition system difficult. Memory size, recording speed, and signal processing capability are major considerations in determining the correct
recording system. Thermal, mechanical, electromagnetic interference, portability, and meteorological factors also influence the selection.
A digital data acquisition system must contain an interface, which is a system involving one or several analog-to-digital converters and, in the case of
multi-channel inputs, a multiplexer. In modern systems, the interface also provides excitation for transducers, calibration, and conversion of units. Many data
acquisition systems are designed to acquire data rapidly and store large records
of data for later recording and analysis. Once the input signals have been digitized, the digital data are essentially immune to noise and can be transmitted
over great distances.
One of the most frequently used temperature transducers is the thermocouple. These are commonly used to monitor temperature with PC-based DAS.
Thermocouples are very rugged and inexpensive and can operate over a wide
temperature range. A thermocouple is created whenever two dissimilar metals
touch and the contact point produces a small open-circuit voltage as a function
of temperature. This thermoelectric voltage is known as the Seebeck voltage,
named after Thomas Seebeck, who discovered it in 1821. The voltage is nonlinear with respect to temperature. However, for small changes in temperature,
the voltage is approximately linear:
where
V  change in voltage.
S  Seebeck coefficient.
T  change in temperature.

∆V ≈ S∆T

(4.36)

248 Performance of Solar Collectors
The Seebeck coefficient (S) varies with changes in temperature, causing the
output voltages of thermocouples to be nonlinear over their operating ranges.
Several types of thermocouples are available; these thermocouples are designated by capital letters that indicate their composition. For example, a J-type
thermocouple has one iron conductor and one constantan (a copper-nickel alloy)
conductor.
Information from transducers is transferred to a computer-recorder from the
interface as a pulse train. Digital data are transferred in either serial or parallel
mode. Serial transmission means that the data are sent as a series of pulses, 1 bit
at a time. Although slower than parallel systems, serial interfaces require only
two wires, which lowers their cabling cost. The speed of serial transmissions is
rated according to the baud rate. In parallel transmission, the entire data word is
transmitted at one time. To do this, each bit of a data word has to have its own
transmission line; other lines are needed for clocking and control. Parallel mode
is used for short distances or when high data transmission rates are required.
Serial mode must be used for long-distance communications where wiring costs
are prohibitive.
The two most popular interface bus standards currently used for data transmission are the IEEE 488 and the RS232 serial interface. Because of the way
the IEEE 488 bus system feeds data, its bus is limited to a cable length of 20 m
and requires an interface connection on every meter for proper termination.
The RS232 system feeds data serially down two wires, one bit at a time, so an
RS232 line may be over 300 m long. For longer distances, it may feed a modem
to send data over standard telephone lines. A local area network (LAN) may
also be available for transmitting information; with appropriate interfacing,
transducer data are available to any computer connected to the local network.

4.9.1 Portable Data Loggers
Portable data loggers generally store electrical signals (analog or digital) to
internal memory storage. The signal from connected sensors is typically stored
to memory at timed intervals, which range from MHz to hourly sampling. Many
portable data loggers can perform linearization, scaling, or other signal conditioning and permit logged readings to be either instantaneous or averaged values. Most modern portable data loggers have built-in clocks that record the time
and date, together with transducer signal information. Portable data loggers
range from single-channel input to 256 or more channels. Some general-purpose
devices accept a multitude of analog or digital inputs or both; others are more
specialized to a specific measurement (e.g., a portable pyranometer with built-in
data logging capability) or for a specific application (e.g., temperature, relative
humidity, wind speed, and solar radiation measurement with data logging for
solar system testing applications). Stored data are generally downloaded from
portable data loggers using a serial or USB interface with a temporary direct
connection to a personal computer. Remote data loggers may also download the
data via modem through telephone lines.

Exercises 249

Exercises
4.1

4.2
4.3

4.4

4.5

4.6

4.7

For seven collectors in series, each 1.2 m2 in area, FR1UL1  7.5 W/m2-°C,
and FR1()1  0.79 at a flow rate of 0.015 kg/s-m2, estimate the useful
energy collected if water is circulated through the collectors, the available
solar radiation is 800 W/m2, and the T (Ti  Ta) is equal to 5°C.
Repeat Example 4.2 for September 15 considering that the weather conditions are the same.
Find the FR()n and FRUL for a collector 2.6 m2 in area with the following hour-long test results.
Qu (MJ)

It (MJ/m2)

Ti (°C)

Ta (°C)

6.05

2.95

15.4

14.5

1.35

3.05

82.4

15.5

For a collector with FR()n  0.82 and FRUL  6.05 W/m2-°C, find the
instantaneous efficiency when Ti  Ta. If the instantaneous efficiency is
equal to 0, Ta  25 °C, and Ti  90 °C, what is the value of solar radiation falling on the collector?
The data from an actual collector test are shown in the following table.
If the collector area is 1.95 m2 and the test flow rate is 0.03 kg/s, find the
collector characteristics F�R()n and FRUL.
Number

Gt (W/m2)

Ta (°C)

Ti (°C)

To (°C)

1

851.2

24.2

89.1

93.0

2

850.5

24.2

89.8

93.5

3

849.1

24.1

89.5

93.3

4

855.9

23.9

78.2

83.1

5

830.6

24.8

77.9

82.9

6

849.5

24.5

77.5

82.5

7

853.3

23.9

43.8

52.1

8

860.0

24.3

44.2

52.4

9

858.6

24.5

44.0

51.9

For a 5.6 m2 collector with F  0.893, UL  3.85 W/m2-°C, ()av 
0.79, and flow rate  0.015 kg/m2-s, find FR, Qu, and efficiency when
water enters at 35°C, the ambient temperature is 14.2°C, and It for the
hour is 2.49 MJ/m2.
The characteristics of a 2 m2 water-heating collector are FR()n  0.79
and FRUL  5.05 W/m2-°C. If the test flow rate is 0.015 kg/m2-s, find the
corrected collector characteristics when the flow rate through the collector
is halved.

250 Performance of Solar Collectors
4.8

4.9

The characteristics of a water-heating collector are FR()n  0.77,
FRUL  6.05 W/m2-°C, and bo  0.12. The collector operates for
a complete day, which has the characteristics shown in the following
table. Find, for each hour, the useful energy collected per unit of aperture area and the collector efficiency. Also estimate the daily efficiency.
Time

It (kJ/m2)

Ta (°C)

Ti (°C)

 (°)

8–9

2090

18.5

35.1

60

9–10

2250

20.3

33.2

47

10–11

2520

22.6

30.5

35

11–12

3010

24.5

29.9

27

12–13

3120

26.5

33.4

25

13–14

2980

23.9

35.2

27

14–15

2490

22.1

40.1

35

15–16

2230

19.9

45.2

47

16–17

2050

18.1

47.1

60

For one cover collector system with KL  0.037 and n  0.92, estimate incidence angle modifier constant (bo) based on () at normal
incidence and at   60°. The cover is made from glass with n  1.526.